Question

Let f(x) = x² + 11x + 25 Find a so that f(a) = 1

Answer 1

A=-3

A=-8

Explanation

Step 1

$f(x)=x^2+11x+25$

there is a number A so f(A) =1, then

$\begin{gathered} f(A)=A^2+11A+25 \\ f(A)=1 \\ \text{then} \\ A^2+11A+25=1 \\ A^2+11A+24=0\text{ equation(1)} \end{gathered}$

Step 2

solve using the quadratic equation

$\begin{gathered} \text{for } \\ ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}$

a)let

a=1

b=11

c=24

the variable is A,

b) replace

$\begin{gathered} A=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ A=\frac{-11\pm\sqrt[]{121^{}-4\cdot1\cdot24}}{2\cdot1} \\ A=\frac{-11\pm\sqrt[]{121^{}-96}}{2} \\ A=\frac{-11\pm\sqrt[]{25}}{2} \\ A_1=\frac{-11+\sqrt[]{25}}{2}=\frac{-11+5}{2}=\frac{-6}{2}=-3 \\ A_1=-3 \\ A_2=\frac{-11-\sqrt[]{25}}{2}=\frac{-11-5}{2}=\frac{-16}{2}=-8 \\ A_2=-8 \end{gathered}$

I hope this helps you